Question

Find a function of the form A sin(Bt – C) that will match the graph below.

Answer 1

No, this one is short answer.

Answer 2

3 and -3?

Answer 3

Would it be 4?

Answer 4

.........

Answer 5

2pi?

Answer 6

I have no idea.

Answer 7

if you use the equation
y = A sin (Bt - C) then the phase shift is C/B

Answer 8

or the horizontal shift , i should say ,
the period is 2pi / B

Answer 9

so I see that you have a horizontal shift of 1, the period is 8 (because half the period is 4)
so i get
y = 3 sin (2pi/8 ( x -1 ) )

Answer 10

now since they want it in the form
y = A sin (Bt - C), then distribute the 2pi/8

Answer 11

y = 3 sin (2pi/8 x -2pi/8 )

Answer 12

y = 3 sin (pi/4 x - pi/4)

Answer 13

Thank you for explaining.

Answer 14

I prefer the form
y = A sin (B ( x - m ) ) + D , notice the parentheses here
in this form, m is the horizontal shift

Answer 15

Can you tell me if I am doing another correctly?

Answer 16

A is amplitude, B = 2pi / period , m is horizontal shift, and D is vertical shift

Answer 17

ok

Answer 18

Now find a function of the form Acos(Bt – C) that will match the graph below.

Answer 19

its the same one

Answer 20

same graph?

Answer 21

First of all, is there something different you are supposed to do if it is cos?

Answer 22

Yes, same graph.

Answer 23

cos has a different graph than sine, so we have to imagine transforming the cos function (moving the cos function)

Answer 24

y = cos x starts its maximum when x = 0 ,